Dynamic domain decomposition method based on weighted Voronoi diagrams

Dynamic load balancing during the high performance computing is an important part of parallel workflow. An efficient way to achieve the desired distribution of load during computation is to use the Voronoi diagram (VD) for the domain decomposition. The advantage of this approach is that it can be used in conjunction with various numerical methods and balancing strategies. Domain decomposition based on Voronoi diagrams can be used together with Eulerian meshes, Lagrangian meshes, and meshfree methods, such as molecular dynamic or smoothed-particle hydrodynamics (SPH). However, for the basic VD decomposition it may be difficult to obtain load balance when the adaptive mesh refinement (AMR) is used: because of the high heterogeneity of the load on the adapted mesh, the balancing algorithms may be unstable or have poor convergence. In the present study we propose an improvement of the ordinary VD domain decomposition method with using the weighted Voronoi diagrams. We demonstrate the possibilities of such domain decomposition to achieve a better balanced configuration on two- and three-dimensional problems using mesh configurations typical for computational fluid dynamics.